i have no idea how to even start this question....
my only clue so far is that f'(A)= -Sin(A)
and that Sin 60°-Sin 45° = Sin 15°
Sin15° + SIn15° + Sin1°= Sin 31°
Sin 60°-Sin1°=Sin59°

I would suggest using the standard identities for cos(A + B) and cos(A - B) applied to cos(30 + 1) and so on (but in radians not degrees), combined with the small angle approximations [email protected] = @ and [email protected] = 1.